A rectangular prism has a volume of 36 inches cubed. If a rectangular pyramid has a base and height congruent to the prism, what is the volume of the pyramid?

Answer 1

Since both the rectangular prism and rectangular pyramid have bases and heights congruent to each other, they are similar shapes. This means their volumes are related by a scale factor.

The volume of a rectangular prism is given by the formula V = lwh, where l is the length, w is the width, and h is the height.

Given that the volume of the rectangular prism is 36 inches cubed, we can set up the equation: 36 = lwh.

Since the rectangular prism has a base and height congruent to the rectangular pyramid, the volume of the pyramid will be one-third of the volume of the prism.

Therefore, the volume of the rectangular pyramid is 36 / 3 = 12 inches cubed.